2006-2007, Term 2 (Winter)

MA3F4 - Linear Analysis

on Thursday 31 May, 2-4pm and 5-6pm, in B2.06.

Here is the official site from the department.

Time & Place: Tue 12-1 in MS.04, Fri 2-4 in MS.05.

Support classes: Tue 10-11 in MA_B3.01, by Michael Doré.

3-hour examination.

Linear Analysis extends Linear Algebra to infinite dimensional vector spaces. Functions form linear spaces of infinite dimension, and differentiation is a linear operation. Among the numerous applications of linear analysis is the study of ODE's and PDE's.
We will introduce Banach and Hilbert spaces, and linear maps (operators) between them. Four major theorems will be discussed: Hahn-Banach, uniform boundedness (Banach-Steinhaus), open mapping, and closed graph. These theorems have interesting consequences, in particular regarding the spectrum of linear operators.

  1. Banach spaces
  2. Baire Category Theorem and its consequences
  3. Hilbert spaces
  4. Bounded operators in Hilbert spaces
  5. Unbounded operators

assignment 1
assignment 2 (19.01.07)
assignment 3
assignment 4
assignment 5
assignment 6
assignment 7
assignment 8
assignment 9